JPMorgan Chase & Co. has invested in a fund that has bought about $400 million in Twitter Inc. shares, valuing the blogging service at as much as $4.5 billion, three people with knowledge of the matter said.

The fund, which has more than $1 billion, is being run by Twitter investor Chris Sacca, said two of the people, who declined to be identified because the arrangement isn’t public. JPMorgan is committing the bulk of the financing for the fund, the people said.

The probes are focused on improper home repossessions and flawed — and sometimes illegal — foreclosure practices. Investigations were launched last fall after the nation’s largest lenders voluntarily halted home seizures when defective document practices — like so-called “robo-signing” — came to light, erupting into a national scandal. State officials, Obama administration policy makers and bankers are discussing possible settlements this week in a hotel outside Washington, D.C.

Re: Fixed-Rate, Low-Rate Mortgages As An Element of Compensation for Foreclosure Fraud

Dear Chairwoman Bair:

I write to you regarding fraud by banks in foreclosures. I previously wrote to you in January, 2010, regarding massive foreclosure fraud.

I am the woman who was featured on the 60 Minutes segment on April 3, 2011 on foreclosure fraud. That segment brought the wrath of Deutsche Bank and American Home Mortgage Servicing down upon me, but I have no regrets. You were also interviewed by Scott Pelley in this segment.

One proposal you recommend for holding the banks accountable for frauds and abuses in foreclosures is to create a fund to make reparations to victims. I support such a fund. An inquiry into whether the victims have been compensated is a traditional part of white collar criminal law. Such compensation is not made, of course, in place of criminal sanctions, but as an important part of such sanctions.

The fraud is so pervasive that twenty or thirty billion dollars will not begin to compensate the victims, and the banks certainly know this, even as they are setting aside as little as one to two billion for such relief.

I am writing to suggest to you that real compensation will include the opportunity for victims to have another mortgage.

Many victims of foreclosure fraud have been left with ruined finances, no credit and deficiency judgments. A one-time cash payout will not repair this damage.

The banks need to be required to offer victims of foreclosure fraud fixed rate, low-rate (3% – 4%) traditional 30-year mortgages, with a 5% down payment.

Such relief should be offered in every case where the lenders have filed forged and fabricated documents in official county records and court cases.

This relief should also be offered wherever a mortgage payment was incorrectly “adjusted” by mortgage servicers, including the tens of thousands of cases where the servicers attempted to justify their actions as a permitted increase in the escrow fund for taxes or insurance.

Such relief should also be offered wherever banks foreclosed while telling homeowners they were considering their eligibility for HAMP.

Such relief should also be offered wherever banks “lost” the homeowners’ HAMP applications and supporting documents three or more times.

Many victims of foreclosure fraud sold their homes, often at a loss, to avoid foreclosure. These victims also need to be compensated. These homeowners were very regularly told that mortgage-backed trusts owned their mortgages and would foreclose, even as the bank trustees knew that the documents demonstrating such ownership, the properly endorsed notes and assigned mortgages, were never held by the trusts.

Not every victim would choose another mortgage because many individuals will never trust another bank. There will, however, be tens of thousands of victims who are willing to become homeowners again.

Communities with a 40% rate of abandoned, vacant homes would benefit from such relief. County and state budgets would also benefit.

Please consider mortgage availability as an integral part of any plan to compensate victims of foreclosure fraud.

A fund run by J.P. Morgan Chase & Co. is in talks with Twitter Inc. to take a minority stake in the rapidly growing microblogging company, people familiar with the matter said.

The investment, which is expected to value Twitter at more than $4 billion, will be made from the bank’s new $1.2 billion digital growth fund, these people said. Exact terms of the potential deal couldn’t be learned.

Discussions between J.P. Morgan and Twitter are continuing, and there is no guarantee a deal will be struck, the people added.

J.P. Morgan also has purchased a significant amount of Twitter’s shares on exchanges for private-company stock, separate from its talks for a direct stake in the company, said a person familiar with the matter.